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Quantitative Radiobiology for Proton Therapy
6.3.11 Taking RBE uncertainty into account in fractionation 6-20
6.4 The use of the linear quadratic model with large fraction sizes 6-22
6.5 Optimisation of fractionation using calculus methods 6-22
6.6 Other contributions to fractionation 6-25
6.7 Summary 6-28
References 6-28
7 The scientific case for using a variable proton RBE rather
7-1
than a constant RBE
7.1 Introduction 7-2
7.1.1 Arguments to preserve the status quo or avoid using RBE 7-3
7.1.2 Justification of a variable RBE 7-4
7.2 Discussion 7-12
7.2.1 Inclusion of flexible RBEs in treatment plans 7-14
References 7-16
8 A general RBE linear energy-efficiency model for protons
8-1
and light ions
8.1 Introduction 8-2
8.2 The available experimental data and its important limitations 8-4
8.3 Description of the Z-specific model 8-5
8.3.1 The relationship between Z and LET
U
8.3.2 Changes in the radiosensitivities with LET 8-6
8.3.3 Obtaining α
8.3.4 An alternative method which does not use LET
and βHvalues 8-8
H
but the
U
slope of the radiosensitivity or measured RBE increments
with increasing LET (up to the turnover point)
8.3.5 The RBE at any specified dose per fraction 8-10
8.4 The graphical results 8-10
8.4.1 Radiosensitivity data 8-10
8.4.2 Fits to experimental RBE data sets 8-13
8.4.3 Applications of the model to clinical radiobiology 8-18
8.5 Further investigations: properties of LET
U
8.6 Conclusions and what remains to be done 8-22
References 8-25
8-5
8-9
8-18
x
Quantitative Radiobiology for Proton Therapy
9 Inclusion of the energy-efficiency LET and RBE model in
9-1
proton therapy
9.1 Introduction 9-1
9.2 RBE uncertainties 9-3
9.3 Description of the quantitative model 9-4
9.4 RBE graphical examples 9-11
9.5 Some comparisons with experimental data sets 9-13
9.6 Two clinical examples where PBT could be sub-optimal 9-15
9.6.1 Prostate cancer 9-15
9.6.2 Paediatric cancers and other radiosensitive tumours such as
lymphomas
9.7 Prediction of tumour response from the RBE increment 9-15
9.8 Intensification of dose rates 9-16
9.9 Concluding discussion 9-19
References 9-20
10 Proton therapy risk assessment using small increments in
9-15
10-1
RBE in the central nervous system and estimation of
remission times
10.1 Introduction 10-2
10.2 Methods 10-4
10.3 Results 10-6
10.3.1 Remission duration considerations 10-7
10.4 Discussion 10-9
10.5 Conclusions 10-12
References 10-12
11 Radiobiological interpretation of the finding of RBE changes
11-1
within similar SOBPs placed at superficial and deep locations
in passively scattered beams but not in scanned pencil beams
11.1 Introduction 11-2
11.2 Methods 11-3
11.2.1 Linear quadratic model base equations 11-3
11.2.2 The modelling method 11-4
11.3 Results 11-6
11.4 Discussion 11-6
11.5 Conclusions 11-8
References 11-9
xi
Quantitative Radiobiology for Proton Therapy
12 Particle therapy dose–time compensations in unintended
12-1
interruptions and re-treatments
12.1 Introduction 12-1
12.2 Unintended treatment interruptions 12-2
12.2.1 Background 12-2
12.2.2 Treatment delays 12-3
12.2.3 Calculations for compensation of treatment interruptions 12-3
12.2.4 Calculations using a variable RBE value 12-6
12.2.5 Comparison of the two methods 12-8
12.2.6 Summary for unintended treatment gap corrections 12-11
12.3 Re-treatments 12-11
12.3.1 Background 12-11
References 12-14
13 Errors of Bragg peak positioning and their radio-biological
13-1
correction
13.1 Introduction 13-1
13.1.1 Further abbreviations and definitions 13-2
13.1.2 Background considerations 13-3
13.1.3 Brief description of methods 13-3
13.2 Model description 13-4
13.2.1 Biological effective dose equations 13-4
13.2.2 Assessment of BED changes after an error 13-6
13.2.3 Worked examples of errors and their correction 13-9
13.2.4 The potential impact of erroneous fractions on tumour
control
13.3 Conclusions 13-15
References 13-16
13-11
14 What remains to be done: including FLASH dose rates and
14-1
conclusions
14.1 Introduction 14-2
14.2 Dose escalation where circumstances permit 14-3
14.3 Simultaneous ‘sensitisation’ effects by new therapies 14-6
14.4 Sensitivity analysis of the energy-efficiency model 14-8
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Quantitative Radiobiology for Proton Therapy
14.5 What could be achieved in a single international laboratory
14-10
dedicated to high-LET radiobiology
14.5.1 Simulated experiments 14-10
14.5.2 Uniqueness of LET
for each ion species 14-14
U
14.5.3 Priority in radiobiological experiments 14-15
14.6 Some untested situations 14-20
14.7 Conclusions 14-20
References 14-21
xiii
Preface
The second edition of this book is intended to cover the principles covering the
potential advantages and pitfalls of proton therapy, especially its radiobiological
modelling applications: for these to be understood, it is essential to present
summaries of radiotherapy, radiobiology, clinical radiobiological modelling for
conventional radiotherapy techniques as well as for protons and other ion beams.
Radiobiological modelling has proved useful in radiotherapy, especially in situations
where departures from protocols occur for a variety of reasons such as unintended
treatment interruptions, errors in treatment delivery, dose-rate effect applications,
comparisons of different techniques, dose-fractionation schedules, re-treatments and
even in clinical trial design. These techniques, if suitably adapted, are capable of
producing similar insights and practical guidelines in proton and other forms of ion
beam therapy. The optimisation of proton and ion beam therapy is essential since
there is considerable ‘competition’ from the more advanced forms of megavoltage
photon-based radiotherapy, which allows fewer and highly focussed treatments to be
given as well as being more economical.
The use of relatively simple mathematics and some very basic worked examples
are included within the text, but has been kept to a minimum, so that all the relevant
disciplines can understand the principles and then use the historical content and
advice provided to develop the subject further. A basic knowledge of radiation
biology is assumed, but references have been kept to the minimum necessary. The
parameters chosen for exploratory modelling and illustrative purposes may require
modification and further input for more specific clinical applications. Any errors are
the sole responsibility of the author. There is inevitably some degree of repetition
where this is considered essential.
The main approach has been to use the biological effective dose (BED) concept
based on the linear quadratic (LQ) model of radiation effect. In recent years it has
been possible to assess the BED values of charged-particle therapies such as protons
and light ions by incorporation of the maximum and minimum limits of the relative
biological effect (RBE), which accounts for the increasing complexity of DNA
damage and the increasing proportion of non-repairable damage that occurs when
the linear energy transfer (LET) of a radiation is increased. Typically LET increases
within the Bragg peak region for charged particles, with resultant increments in
RBE, but the RBE reduces with increasing dose and also at very high LET values;
and it is important to realise that different biosystems will have quite different RBE
values. The topic of RBE remains controversial, although it is being increasingly
understood, and there are several models that attempt to link LET with RBE, many
of which use formidable mathematics. In contrast, this book addresses how to
achieve this by using relatively simple mathematics. Such a simpler approach can be
understood by physicians, physicists and biologists. More complex approaches can
be limited in their usefulness due to excessive and/or restrictive assumptions and the
limits of what can be known. Simpler models, although they must always need
xiv
Quantitative Radiobiology for Proton Therapy
caveats, are capable of providing useful qualitative and quantitative understanding
of the basic principles which govern clinical outcomes.
This subject is as such multi-disciplinary, and based on a triangular arrangement
with physics, medicine and biology forming the apices of an isosceles triangle
(figure P.1). The decisive middle ground has to be covered by individuals who have
sufficient knowledge and experience of all three disciplines. A basic knowledge of these
three subjects and the inter-disciplinary subject of radiation biology is assumed, along
with basic aspects of particle therapy such as the Bragg peak effect, the characteristics
of the spread-out Bragg peak (SOBP) and how this may be achieved. The author is
minded that the text should be reasonably understood by members of all these
disciplines, although additional reading will be required from review articles and
textbooks to supplement cross-disciplinary understanding. Also, that each primary
discipline is divided into a spectrum of further specialisation groups: physicists, split
into fundamental particle physicists, accelerator or detector physicists and their
medical physicist colleagues; in biology, there are purely molecular biologists (biochemists) concerned with in vitro work, biophysicists (physiologists), pharmacologists
and zoologists, some concerned with in vivo animal testing; and within the faculties of
medicine, the knowledge base is spread over anatomy, all forms of pathophysiology,
oncology, surgery, patient management as well as a broad interest in epidemiology.
Also, many non-biologically trained physicists have had a very significant influence in
advancing radiobiology and that, given the added complexities of charged-particle
physics, their continued involvement will be essential to understanding particle
therapy and its associated radiobiology.
Figure P.1. The central role of multidisciplinary science which must include quantitative radiobiological
modelling.
xv
Quantitative Radiobiology for Proton Therapy
With all these facets in mind, it is necessary to write sympathetically for the nonspecialist, but to furnish sufficient detail regarding many necessary fundamental
aspects across these topics, while providing more detailed information for the
practitioner or researcher in this field. For reasons of space and economy, it has been
necessary to omit the classical graphs and diagrams associated with the basic
sciences, but which can be found in standard textbooks. In most instances, since
most readers of this book will be familiar with these, the brief qualitative
descriptions and definitions provided will act as an aide-mémoire.
The medical decision-makers of the future in particle therapy will need broad
scientific backgrounds, excellent clinical and oncological training, and be able to
appreciate the strengths and weaknesses of the available mathematical models that
link the clinical, biological and physical parameters, and which can be used to
protect the patient against over- or underdosages. Modelling is a necessary way of
quantitative communication between the three apices already referred to, in the
important multi-disciplinary centre ground, complementing rational verbal or
written approaches. In essence, this must be kept sufficiently simple in order for
all disciplines to interact.
Considerable practice is necessary to become familiar and competent in this
subject. The calculations may appear to be deceptively easy, as only knowledge of
some higher school mathematics is necessary, and this can be aided by computer
software systems such as Mathematica, Matlab and Maple. However, some of the
clinically based calculations are quite protracted, with many more pitfalls (due to
RBE, LET, etc.) than for similar calculations in the case of photon-based treatments. To aid the estimation of RBE and isoffective doses, some interactive sections
have been introduced to the text by Dr Moore.
There are many who regard particle therapy as just a seamless extension of
photon-based radiotherapy. This is certainly useful in terms of departmental
organisation within a hospital structure, to ensure good patient access and to
capitalise on site-specialist knowledge of the oncologist in terms of detailed regional
anatomy and indications for therapy. However, owing to the added complexity of
particle therapy, there is an essential need to educate and train all the sub-disciplines
involved in treatment delivery and patient management, in order to inform them of
the strengths and weaknesses of particle therapy, and by knowing these to
continually search for better, highly optimised therapy.
Depending on the background of the reader, it is not necessary to read the whole
of the book. Chapter 1 provides the essential physics background, mostly for the
benefit of biologists and clinicians, but includes the importance of the choice of the
reference radiation in RBE studies as well as the different ways in which LET is
expressed, and introduces the potentially important parameter of inter-track
distance. In chapter 2, the basis of radiobiological modelling is introduced, with
formulations for conventional megavoltage photon radiotherapy and for particle
therapy, including low and high dose, dose-rate variations and the useful BED
concept. Chapters 3 and 4 have been written for persons who have little or no
previous experience of radiotherapy, with discussion of the essential medical aspects
of treatment planning, including the influence of surgery and other factors on tissue
xvi
Quantitative Radiobiology for Proton Therapy
viability. Some of the key historical developments in radiotherapy are covered in
chapter 5, as well as what has been learned from extensive basic and clinical research
using fast neutrons for modern applications with charged particles. Chapter 6
considers dose-fractionation effects in photon and particle therapy, with some
worked examples.
The rationale for using a variable as opposed to the conventional constant RBE
in proton therapy is provided in chapter 7. This is followed by the description of a
relatively simple ‘energy efficiency’ model for estimation of RBE values for any ion
beam in chapter 8. More specific applications in proton therapy are given in
chapter 9, with some tables that suggest tentative RBE allocations for variable
values of LET in different classes of tissues and tumours. Chapter 10 describes a
system for estimating risk in the central nervous system and which is designed to be
user-friendly in that no RBE-LET models are used, and is considered necessary
where the full prescribed proton dose has to be given to a critical normal tissue.
Chapter 11 considers the reductions in RBE which have been found in experimental
work, where passively scattered beam SOBPs are repositioned from superficial to
much deeper positions, whereas no such RBE reductions are found with scanned
pencil beams, with important implications.
The correction of unintended treatment interruptions for high-LET treatments,
with worked examples, is described in chapter 12, which also includes formulations
for assessing re-treatment doses in the central nervous system. Chapter 13 considers
the radiobiological correction of Bragg peak placement errors, resulting in deviations in both LET and dose. Chapter 14 contains further possible future developments to improve our overall understanding and especially to obtain more accurate
modelling parameters, as well as methods of assessing the potential impact of
concomitant drug sensitisation with high-LET radiations.
It is hoped that this book will not only improve the safety and effectiveness of
particle therapies, but also inspire further research and enquiry.
xvii
Acknowledgements
I am extremely grateful for the help and encouragement provided by the following:
1. Many colleagues who have inspired me over many years to seek solutions to
high-LET problems, too large a number to mention individually, but
especially Roger Dale, Gillies McKenna, John Hopewell, Oliver Scott,
Jack Fowler, Mark Hill, Boris Vojnovic, Ken Peach, Claire Timlin,
Herman Suit, Michael Goitein, Tony Lomax, Peter O’Neil, Dudley
Goodhead, Kevin Prise, Stuart Green, Alex Carabe-Fernandez, Karen
Kirkby, David Colling, Douglas Errington, Andrzej Kacperek, Richard
Britten and Hilmar Warenius. Also, to the late Edmund Wilson (CERN) for
stimulating discussions.
2. CERN, Geneva for a Visiting Scientist award during 2014, and to the
Director General for the award of Guest Professor 2015–2016, with the
support of Prof Manjit Dosanjh.
3. The Principals and Fellows of Brasenose College, Oxford 2010–2015,
especially Sir Roger Cashmore, and Green Templeton College as from 2017.
B.J. has been an investigator on several UK Research Council and EU FP-7 funded
grants concerned with particle therapy, including ENVISION (241851),
ENTERVISION (264552), and ULICE (228436), to The Medical Research
Council UK for support to study radiobiology (1980–83) and to The Cyclotron
Trust (2000–05), and advises the European Particle Therapy Network.
Also, to all the journals which have published my work on this subject, and for
reproduction of graphics, some of which are included in this book.
xviii
Author biographies
Bleddyn Jones
After studying Medicine at Cambridge, with some mathematics, and developing an
interest in cancer topics with Dr Donald Cater ScD FRCS, he underwent clinical
and postgraduate training at Guy’s, St Thomas’s, St Bartholomew’s and The Royal
London Hospitals. As part of a Medical Research Council Earmarked Fellowship,
he studied for a London University Radiobiology MSc and then undertook research
in tumour cell kinetics before his clinical oncology training. Consultant and
academic appointments were held at Clatterbridge (University of Liverpool),
Hammersmith (Imperial College) and Birmingham, before becoming Professor of
Clinical Radiation Biology at Oxford University, where his research concentrated
on developing new mathematical models of RBE in particle therapy, as well as retreatments and radiosurgery, all extensions of previous applied research to reduce
toxicity in gynaecological brachytherapy and in brain tumour treatments as part of
long collaborations with Professor R. G. Dale. He helped design and participated in
many teaching courses, such as the Radiobiology MSc at Oxford, on particle
therapy at CERN for many years, and held a Guest Professorship there while acting
as Secretary to the Medical Applications Committee.
Joshua Moore
Joshua Moore graduated in Mathematics at Cardiff University, followed by a PhD
in applied mathematics, supervised by Dr Thomas E. Woolley, primarily focusing
on developing multi-scale mathematical models to investigate organoid formation.
Whilst at Cardiff he won many academic prizes and worked with Professors Jones
and Hopewell on re-treatments using photons, protons and other ions as well as
radiosurgery. His additional research interests are in applying mathematics in
biological areas of sub-cellular dynamics, pattern formation, virology and oncology.
Subsequently, he has been appointed as a post-doctorate Research Associate in the
Mathematical Institute at the University of Oxford, where he is primarily interested
in unravelling the information contained in the spatial properties of cellular biology
to explore questions in cancer detection, optimal treatment planning and cellular
self-organisation, intercellular communication and dynamic tissue morphologies.
For further information, see https://bit.ly/GoogleScholarJWM.
xix